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Calculate K.E., P.E total energy of the ...

Calculate K.E., P.E total energy of the electron in Bohr's first orbit of an hydrogen atom.

Text Solution

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Given n = 1 , Assume other constants
`K.E. = (me^(4))/(8epsilon_(0)^(2)n^(2)h^(2))" "...(1)`
`P.E. = (-me^(4))/(4epsilon_(0)^(2)n^(2)h^(2))-2K.E." "...(2)`
Total energy `= KE+PE " "...(3)`
from (1)
`KE=(9.1xx10^(-31)xx(1.6xx10^(-19))^(4))/(8xx(8.854xx10^(-12))xx1^(2)xx(6.625xx10^(-34))^(2))=2.16xx10^(-18)J`
`=(2.16xx10^(-18))/(1.6xx10^(-18))=13.54eV`
From (2) `PE=-2xx13.54eV=-27.08eV`
From (3) `TE=KE+PE=13.54+(-27.08)=-13.54eV.`
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